Chapter 10 Autoregressive Model Applied to the Meazza Stadium for Damage Detection G. Busca, A. Cigada, and A. Datteo Abstract Aerospace, civil and mechanical structures are naturally exposed to damages, which could depend on several sources, such as environment degradations, design faults or unexpected natural events. Statistical pattern recognition has recently emerged as an effective technique for structural health monitoring. Its success depends on the possibility to detect unusual operational scenarios just through a statistical data processing of the structural vibration measurements and without the need of a physical model. In this paper, we present the application of one of these techniques to the Meazza stadium grandstands, in order to detect different operational and environmental conditions of this structure, by extracting sensitive features from vibration time series. We trained an autoregressive model (AR) on the vibrations data acquired for empty stadium conditions, which were considered the “undamaged” status. Then we tested how this statistical model is able to describe the behaviour of the same structure under different environment conditions, for instance at different temperature values. In the end, we used statistical pattern recognition to detect the “damaged” scenarios represented by the events planned in the stadium, football matches and concerts, when the stands was occupied by public. Keywords Structural health monitoring • Damage detection • Statistical pattern recognition • Autoregressive model • Mahalanobis distance 10.1 Introduction Structural Health Monitoring (SHM) consists in monitoring structures by the use of many sensors and devices to detect the presence of any eventual damage or unusual behaviour. An appropriate SHM system can help to reduce the possibility of catastrophic failure, optimizing maintenance costs, and the downtime for structural rehabilitation. The authors pose the SHM process in the context of a statistical pattern recognition paradigm [1]. The idea is to fix the normal dynamic operating condition of the structure, recording and extracting features from the vibration data during the daily use, and considering this database as the initial state, describing its standard behaviour; then the data obtained by subsequent acquisitions can be examined to check if these features exhibit meaningful drifts from the standard state. The discerning of the standard state from the damage condition has to be done by fixing a threshold between these two cases. It should be noted that these statistic-based techniques do not use finite element models or any others physical models, which are very difficult to be designed for real complex structures, because they often require hard work on intensive tuning and they are often affected by significant uncertainties caused by user interaction and modelling errors. In this paper, we show a SHM application only based on signal statistical analysis from the measured vibration data; this approach is very attractive for the development of an automated health monitoring system when the structures are too complex to be modelled. As a first step, we will process the vibration data acquired from one stand of the Meazza stadium in Milan, by an autoregressive model. For applications on existing structures, data from damaged conditions are often unavailable, at least for structures still used for their original purpose. A database concerning the empty stadium condition is used to set the standard behaviour and to evaluate a threshold of the damage feature for the out-of-normal behaviour recognition. The feature used in this paper is the well-known Mahalanobis distance [2] calculated on the parameters of the autoregressive model. G. Busca • A. Cigada • A. Datteo ( ) Department of Mechanical Engineering, Politecnico di Milano, Via G. La Masa, 1, 20156 Milano, Italy e-mail: alessio.datteo@polimi.it © The Society for Experimental Mechanics, Inc. 2015 C. Niezrecki (ed.), Structural Health Monitoring and Damage Detection, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15230-1_10 97
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